TSTP Solution File: FLD016-3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD016-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 22:27:19 EDT 2023

% Result   : Unsatisfiable 0.20s 0.74s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   47 (  19 unt;  14 typ;   0 def)
%            Number of atoms       :   59 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   54 (  28   ~;  26   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   38 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    sum: ( $i * $i * $i ) > $o ).

tff(decl_23,type,
    additive_identity: $i ).

tff(decl_24,type,
    defined: $i > $o ).

tff(decl_25,type,
    additive_inverse: $i > $i ).

tff(decl_26,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    multiplicative_identity: $i ).

tff(decl_28,type,
    multiplicative_inverse: $i > $i ).

tff(decl_29,type,
    add: ( $i * $i ) > $i ).

tff(decl_30,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_31,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_32,type,
    a: $i ).

tff(decl_33,type,
    b: $i ).

tff(decl_34,type,
    u: $i ).

tff(decl_35,type,
    v: $i ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).

cnf(commutativity_addition,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).

cnf(sum_6,negated_conjecture,
    sum(a,v,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).

cnf(v_is_defined,hypothesis,
    defined(v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).

cnf(sum_5,negated_conjecture,
    sum(a,u,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_5) ).

cnf(u_is_defined,hypothesis,
    defined(u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).

cnf(not_sum_7,negated_conjecture,
    ~ sum(additive_identity,u,v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).

cnf(c_0_10,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_11,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_12,plain,
    ( sum(X1,X2,X3)
    | ~ defined(X3)
    | ~ sum(X1,X4,additive_identity)
    | ~ sum(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_13,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_14,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_15,plain,
    ( sum(additive_inverse(X1),X2,X3)
    | ~ defined(X3)
    | ~ defined(X1)
    | ~ sum(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    sum(a,v,b),
    sum_6 ).

cnf(c_0_17,hypothesis,
    defined(v),
    v_is_defined ).

cnf(c_0_18,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_19,plain,
    ( sum(X1,additive_inverse(X1),additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    sum(additive_inverse(a),b,v),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).

cnf(c_0_21,negated_conjecture,
    sum(a,u,b),
    sum_5 ).

cnf(c_0_22,plain,
    ( sum(X1,X2,additive_identity)
    | ~ defined(X3)
    | ~ sum(X4,additive_inverse(X3),X2)
    | ~ sum(X1,X4,X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    sum(b,additive_inverse(a),v),
    inference(spm,[status(thm)],[c_0_14,c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    sum(u,a,b),
    inference(spm,[status(thm)],[c_0_14,c_0_21]) ).

cnf(c_0_25,hypothesis,
    defined(u),
    u_is_defined ).

cnf(c_0_26,negated_conjecture,
    ( sum(X1,v,additive_identity)
    | ~ sum(X1,b,a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18])]) ).

cnf(c_0_27,negated_conjecture,
    sum(additive_inverse(u),b,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_18]),c_0_25])]) ).

cnf(c_0_28,plain,
    ( sum(X1,X2,X3)
    | ~ defined(X3)
    | ~ defined(X1)
    | ~ sum(additive_inverse(X1),X3,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_19]) ).

cnf(c_0_29,negated_conjecture,
    sum(additive_inverse(u),v,additive_identity),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    sum(u,additive_identity,v),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_17]),c_0_25])]) ).

cnf(c_0_31,negated_conjecture,
    ~ sum(additive_identity,u,v),
    not_sum_7 ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_30]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : FLD016-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 00:40:29 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.74  % Version  : CSE_E---1.5
% 0.20/0.74  % Problem  : theBenchmark.p
% 0.20/0.74  % Proof found
% 0.20/0.74  % SZS status Theorem for theBenchmark.p
% 0.20/0.74  % SZS output start Proof
% See solution above
% 0.20/0.75  % Total time : 0.167000 s
% 0.20/0.75  % SZS output end Proof
% 0.20/0.75  % Total time : 0.170000 s
%------------------------------------------------------------------------------